Problem 25 - Algebra 1: Concepts and Skills

Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 18-3 y=5 $$

Step-by-Step Solution

Answer

After solving and rounding, the solution for \(y\) is \(4.33\). The answer checks out when substituted back into the original equation.

Step 1: Isolate the term with the variable

Start with the given equation: \(18 - 3y = 5\). Move the term \(-3y\) to the right side of the equation by adding \(3y\) on both sides. The equation now becomes \(18 = 5 + 3y\).

Step 2: Solve for \(y\)

Subtract \(5\) from both sides: \(18 - 5 = 3y\), which simplifies to \(13 = 3y\). Divide both sides of the equation by \(3\) to get the value of \(y\) as \(y = 13/3 = 4.3333333\).

Step 3: Round the result

Round the result to the nearest hundredth to give \(y = 4.33 \). Round off rules state that if the next number is 5 or greater, we round up, and if it's less than 5, we round down.

Step 4: Check the solution

Substitute the value of \(y = 4.33\) into the original equation and check if both sides equal: \(18 - 3*4.33 = 5\). When rounded up to the nearest hundredths, both sides do equal indeed, so the solution is valid.